Question

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Given the functions f(n) = 11 and g(n) = ( three over four )n − 1, combine them to create a geometric sequence, an, and solve for the 9th term. (2 points)


an = (11 ⋅ three over four )n − 1; a9 ≈ 24.301

an = 11( three over four )n − 1; a9 ≈ 1.101

an = 11 + ( three over four )n − 1; a9 ≈ 11.100

an = 11 − ( three over four )n − 1; a9 ≈ 9.900

Answer 1

A geometric sequence is a sequence of numbers that follows a pattern where the next term is found by multiplying by a constant called the common ratio, q:

$a_n=a_{n-1}\cdot q=(a_{n-2}\cdot q)\cdot q=a_{n-2}\cdot q^2=...,\\ a_n=a_1\cdot q^{n-1}$.

Given the functions $f(n)=11$ and $g(n)=\left(\dfrac{3}{4}\right)^{n-1}$, you can consider $a_n=11\cdot \left(\dfrac{3}{4}\right)^{n-1}$ as n-th term of the geometric sequence with first term $a_1=11$ and common ratio $q=\dfrac{3}{4}$.

For $n=9$,

$a_9=11\cdot \left(\dfrac{3}{4}\right)^{9-1} =11\cdot \left(\dfrac{3}{4}\right)^8=1.101$.

Answer: the correct choice is B.

Answer 2

Answer:

B

Step-by-step explanation:

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